It does, and it's definitely less sophisticated than mariachi music (as you might expect in this poor and formerly isolated mountain area). I don't know any name except "traditional music from northern New Mexico" or variations of that. But I can ask my Spanish teacher--un músico de Chamisal, a quien le gusta mucho la música folklórica de aquí. (Sorry, had to practice there for a second. A musician from the mountain town of Chamisal, who likes folk music from here a lot.)